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Theorem equtr 1846
Description: A transitive law for equality. (Contributed by NM, 23-Aug-1993.)
Assertion
Ref Expression
equtr  |-  ( x  =  y  ->  (
y  =  z  ->  x  =  z )
)

Proof of Theorem equtr
StepHypRef Expression
1 ax-7 1839 . 2  |-  ( y  =  x  ->  (
y  =  z  ->  x  =  z )
)
21equcoms 1845 1  |-  ( x  =  y  ->  (
y  =  z  ->  x  =  z )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839
This theorem depends on definitions:  df-bi 188  df-ex 1660
This theorem is referenced by:  equtrr  1847  equequ1  1848  equviniv  1853  equvin  1854  ax6e  2056  equvini  2142  sbequi  2169  axsep  4542  bj-axsep  31366
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